Recently, this problem has attracted
intensive interests under the umbrella of distributional robustness [1]}, [2]}, [3]}, [4]}, [5]}, [6]}. Specifically,
let \(P\)  be a joint data distribution over
features \(X \in \mathcal {X}\)  and labels \(Y \in \mathcal {Y}\) ,
and let \(h_\theta : \mathcal {X} \rightarrow \mathcal {Y}\)  be a
machine learning model parameterized by \(\theta \) . For a loss function
\(\ell : \mathcal {Y} \times \mathcal {Y} \rightarrow \mathbb {R}\) , we hope to compute
\(\mathcal {R}_\theta (\mathcal {U}_P) := \sup _{Q \in \mathcal {U}_P}\mathbb {E}_{(X, Y)\sim Q}[\ell (h_\theta (X), Y)]\) 
